Patients with tumors that do not match one of the currently active drug-biomarker combinations receive durvalumab intravenously (IV) over 60 minutes on day 1. Courses repeat every 2 weeks for 12 months in the absence of disease progression or unacceptable toxicity. Upon evidence of progression following discontinuation of 12 months of treatment, patients may restart treatment and continue for up to 12 additional months (Arm III).